Escudero, who started in 26 league games to help Getafe defend their Primera Division status last season, will put pen to paper on a four-year contract with the Europa League winners.
A statement from Sevilla read: “Sevilla FC has agreed with Getafe CF the transfer of Sergio Escudero, subject to the left-back passing a medical next week.
“If all goes well, Escudero will sign a contract with Sevilla for the next four seasons.
Escudero, 25, began his career at Segunda Division club Murcia before joining German side Schalke 04 in the summer of 2010.
He went on loan to Getafe in January 2013 and after his successful spell with the Madrid outfit, he sealed a permanent move to the Coliseum Alfonso Perez that summer.
Sevilla, coached by Unai Emery, finished fifth in La Liga in the 2014-15 campaign but will play in next season’s Champions League after their successful Europa League title defence.